Genericity of Nondegeneracy for Light Rays in Stationary Spacetimes

Given a Lorentzian manifold (M, g), an event p and an observer U in M, then p and U are light conjugate if there exists a lightlike geodesic gamma : [0, 1] -> M joining p and U whose endpoints are conjugate along gamma. Using functional analytical techniques, we prove that if one fixes p and U in a differentiable manifold M, then the set of stationary Lorentzian metrics in M for which p and U are not light conjugate is generic in a strong sense. The result is obtained by reduction to a Finsler geodesic problem via a second order Fermat principle for light rays, and using a transversality argument in an infinite dimensional Banach manifold setup.

On a Gromoll-Meyer type theorem in globally hyperbolic stationary spacetimes

Following the lines of the celebrated Riemannian result of Gromoll and Meyer, we use infinite dimensional equivariant Morse theory to establish the existence of infinitely many geometrically distinct closed geodesics in a class of globally hyperbolic stationary Lorentzian manifolds.

Genericity of Nondegenerate Critical Points and Morse Geodesic Functionals

We consider a family of variational problems on a Hilbert manifold parameterized by an open subset of a Banach manifold, and we discuss the genericity of the nondegeneracy condition for the critical points. Using classical techniques, we prove an abstract genericity result that employs the infinite dimensional Sard-Smale theorem, along the lines of an analogous result of B. White [29]. Applications are given by proving the genericity of metrics without degenerate geodesics between fixed endpoints in general (non compact) semi-Riemannian manifolds, in orthogonally split semi-Riemannian manifolds and in globally hyperbolic Lorentzian manifolds. We discuss the genericity property also in stationary Lorentzian manifolds.

Quantization of unstable linear scalar fields in static spacetimes

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A quasi stationary approach to drying kinetics of cylindrical food particulates in a heat pump asisted fluid bed dryer

Experiments were undertaken to study drying kinetics of moist cylindrical shaped food particulates during fluidised bed drying. Cylindrical particles were prepared from Green beans with three different length:diameter ratios, 3:1, 2:1 and 1:1. A batch fluidised bed dryer connected to a heat pump system was used for the experimentation. A Heat pump and fluid bed combination was used to increase overall energy efficiency and achieve higher drying rates. Drying kinetics, were evaluated with non-dimensional moisture at three different drying temperatures of 30, 40 and 50o C. Numerous mathematical models can be used to calculate drying kinetics ranging from analytical models with simplified assumptions to empirical models built by regression using experimental data. Empirical models are commonly used for various food materials due to their simpler approach. However problems in accuracy, limits the applications of empirical models. Some limitations of empirical models could be reduced by using semi-empirical models based on heat and mass transfer of the drying operation. One such method is the quasi-stationary approach. In this study, a modified quasi-stationary approach was used to model drying kinetics of the cylindrical food particles at three drying temperatures.

Prediction of fluidization behaviour and a quasi-stationary approach to drying kinetics of irregular particulate food materials

Changes in fluidization behaviour behaviour was characterised for parallelepiped particles with three aspect ratios, 1:1, 2:1 and 3:1 and spherical particles. All drying experiments were conducted at 500C and 15 % RH using a heat pump dehumidifier system. Fluidization experiments were undertaken for the bed heights of 100, 80, 60 and 40 mm and at 10 moisture content levels. Due to irregularities in shape minimum fluidisation velocity of parallelepiped particulates (potato) could not fitted to any empirical model. Also a generalized equation was used to predict minimum fluidization velocity. The modified quasi-stationary method (MQSM) has been proposed to describe drying kinetics of parallelepiped particulates at 30o C, 40o C and 50o C that dry mostly in the falling rate period in a batch type fluid bed dryer.

A quasi-stationary approach to drying kinetics of different shaped food particulates in a heat pump assisted by fluid bed dryer

Experiments were undertaken to study drying kinetics of different shaped moist food particulates during heat pump assisted fluidised bed drying. Three particular geometrical shapes of parallelepiped, cylindrical and spheres were selected from potatoes (aspect ratio = 1:1, 2:1, 3:1), cut beans (length: diameter = 1:1, 2:1, 3:1) and peas respectively. A batch fluidised bed dryer connected to a heat pump system was used for the experimentation. A Heat pump and fluid bed combination was used to increase overall energy efficiency and achieve higher drying rates. Drying kinetics, were evaluated with non-dimensional moisture at three different drying temperatures of 30, 40 and 50o C. Due to complex hydrodynamics of the fluidised beds, drying kinetics are dryer or material specific. Numerous mathematical models can be used to calculate drying kinetics ranging from analytical models with simplified assumptions to empirical models built by regression using experimental data. Empirical models are commonly used for various food materials due to their simpler approach. However problems in accuracy, limits the applications of empirical models. Some limitations of empirical models could be reduced by using semi-empirical models based on heat and mass transfer of the drying operation. One such method is the quasi-stationary approach. In this study, a modified quasi-stationary approach was used to model drying kinetics of the cylindrical food particles at three drying temperatures.

Spectrum sensing, detection and optimisation in cognitive radio for non-stationary primary user signals

Cognitive radio is an emerging technology proposing the concept of dynamic spec- trum access as a solution to the looming problem of spectrum scarcity caused by the growth in wireless communication systems. Under the proposed concept, non- licensed, secondary users (SU) can access spectrum owned by licensed, primary users (PU) so long as interference to PU are kept minimal. Spectrum sensing is a crucial task in cognitive radio whereby the SU senses the spectrum to detect the presence or absence of any PU signal. Conventional spectrum sensing assumes the PU signal as ‘stationary’ and remains in the same activity state during the sensing cycle, while an emerging trend models PU as ‘non-stationary’ and undergoes state changes. Existing studies have focused on non-stationary PU during the transmission period, however very little research considered the impact on spectrum sensing when the PU is non-stationary during the sensing period. The concept of PU duty cycle is developed as a tool to analyse the performance of spectrum sensing detectors when detecting non-stationary PU signals. New detectors are also proposed to optimise detection with respect to duty cycle ex- hibited by the PU. This research consists of two major investigations. The first stage investigates the impact of duty cycle on the performance of existing detec- tors and the extent of the problem in existing studies. The second stage develops new detection models and frameworks to ensure the integrity of spectrum sensing when detecting non-stationary PU signals. The first investigation demonstrates that conventional signal model formulated for stationary PU does not accurately reflect the behaviour of a non-stationary PU. Therefore the performance calculated and assumed to be achievable by the conventional detector does not reflect actual performance achieved. Through analysing the statistical properties of duty cycle, performance degradation is proved to be a problem that cannot be easily neglected in existing sensing studies when PU is modelled as non-stationary. The second investigation presents detectors that are aware of the duty cycle ex- hibited by a non-stationary PU. A two stage detection model is proposed to improve the detection performance and robustness to changes in duty cycle. This detector is most suitable for applications that require long sensing periods. A second detector, the duty cycle based energy detector is formulated by integrat- ing the distribution of duty cycle into the test statistic of the energy detector and suitable for short sensing periods. The decision threshold is optimised with respect to the traffic model of the PU, hence the proposed detector can calculate average detection performance that reflect realistic results. A detection framework for the application of spectrum sensing optimisation is proposed to provide clear guidance on the constraints on sensing and detection model. Following this framework will ensure the signal model accurately reflects practical behaviour while the detection model implemented is also suitable for the desired detection assumption. Based on this framework, a spectrum sensing optimisation algorithm is further developed to maximise the sensing efficiency for non-stationary PU. New optimisation constraints are derived to account for any PU state changes within the sensing cycle while implementing the proposed duty cycle based detector.

Advantages of tandem LC-MS for the rapid assessment of tissue-specific metabolic complexity using a pentafluorophenylpropyl stationary phase

In this study, a tandem LC-MS (Waters Xevo TQ) MRM-based MS method was developed for rapid, broad profiling of hydrophilic metabolites from biological samples, in either positive or negative ion modes without the need for an ion pairing reagent, using a reversed-phase pentafluorophenylpropyl (PFPP) column. The developed method was successfully applied to analyze various biological samples from C57BL/6 mice, including urine, duodenum, liver, plasma, kidney, heart, and skeletal muscle. As result, a total 112 of hydrophilic metabolites were detected within 8 min of running time to obtain a metabolite profile of the biological samples. The analysis of this number of hydrophilic metabolites is significantly faster than previous studies. Classification separation for metabolites from different tissues was globally analyzed by PCA, PLS-DA and HCA biostatistical methods. Overall, most of the hydrophilic metabolites were found to have a "fingerprint" characteristic of tissue dependency. In general, a higher level of most metabolites was found in urine, duodenum, and kidney. Altogether, these results suggest that this method has potential application for targeted metabolomic analyzes of hydrophilic metabolites in a wide ranges of biological samples.

Eight weeks of episodic visual navigation inside a non-stationary environment using adaptive spherical views

This paper presents a long-term experiment where a mobile robot uses adaptive spherical views to localize itself and navigate inside a non-stationary office environment. The office contains seven members of staff and experiences a continuous change in its appearance over time due to their daily activities. The experiment runs as an episodic navigation task in the office over a period of eight weeks. The spherical views are stored in the nodes of a pose graph and they are updated in response to the changes in the environment. The updating mechanism is inspired by the concepts of long- and short-term memories. The experimental evaluation is done using three performance metrics which evaluate the quality of both the adaptive spherical views and the navigation over time.